Question

Conductivity of a solution is directly proportional to:
A. Dilution
B. Number of ions
C. Current Density
D. Volume of the Solution

Answer 1

Hint: Conductance is the degree to which an object or a conductor can conduct the electric current through it. Conductivity is the fundamental property of electrolytes. It is the measurement of an ability of an aqueous solution to conduct electricity. Try to understand ions are the current carried in an aqueous solution and there is some relation between conductivity and ions.

Complete answer:
According to Ohm’s Law, Resistance is directly proportional to the length and inversely proportional to area of cross-section of conductor. If $l$ is the length and $a$ is the area of cross section then $R$ resistance is
$R \propto \dfrac{l}{a}$
$R = \rho \dfrac{l}{a}$
Where $\rho $is the resistivity of the conductor
Conductance $G$ is the reciprocal of resistance $R$ and conductivity $\kappa $ is reciprocal of resistivity $\rho $’
$G = \kappa \dfrac{a}{l}$
$\kappa = G\dfrac{l}{a}$
$\dfrac{l}{a}$ is called the cell constant of the conductivity cell where $l$ is the distance between the two electrodes and $a$ is the area of cross-section.
The conductivity of all electrolytes always decreases with the decrease in concentration because it is the conductance of the ions present in unit volume and the number of ions per unit volume decreases with decrease in concentration.
According to the options given,
A. Dilution – on dilution the concentration of the electrolyte solution decreases, therefore it conductivity decreases because the degree of dissociation increases but the number of ions per unit volume decreases. The conductivity is inversely proportional to dilution.
B. Number of ions – this is the correct option. Since the conductivity is directly proportional to the number of ions per unit volume.
C. Current Density – is the amount of current flowing through unit cross- sectional area. The conductivity is independent of the current density.
D. Volume- On increasing the volume, the number of ions per unit volume decreases. Hence conductivity is inversely proportional to volume.
Therefore, the correct answer is option (B).

Note:
Conductivity depends on the number of ions present per unit volume because it is the ions in an electrolytic cell that carry currents and not the electrons. Conductance is different from conductivity. Conductance if mobility of the ions increases in case of dilution but conductivity decreases.